Section Modulus calculation and optimization

Section Modulus calculation and Optimization

Section modulus is a ratio of Area moment of Inertia about a neutral axis and to the distance of Outermost fibre from the neutral Axis.

Z=I/y

Where as, Z= section Modulus.

I= Area Moment of Inertia.

y= Distance from Neutral Axis to the outermost Fibre.

unite is Cubic mm or Cubic m

Bending Euation

from therory of Simple Bending

M = Bending Moment (N - mm)

I = Moment of Inertia mm⁴

σ = Bending Stress N / mm²

y = ( D / 2 ) Distance From Neutral Axis (mm)

E = Modulus of Elasticity (N /mm²)

R = Radius of Curvature (mm)

σ = M/I*y= M/(I/y)=M/Z

bending stress (σ) induced in member is inversly proportional to the Section Modulus (Z).

lets Calculate Section Modulus For Two Beams, Which having Same Cross Sectionm Area and same Bending Moment.

here is two beams, Beam A and Beam B

formula for Section Modulus (Z)=I/y

Area Moment Of Inertia (I) =(bd^3)/12

from Above relations

Z of Beam A >> Z of Beam B

here in image you can see deflections of same flat beam under different loading Conditions.

Procedure:

first created plane at center of Hood from Vehicle X direction. taken Intersection of Hood inner panel, hood outer panel to the that Center plane.

then sketched and closed the section to do Analysis

then Used Section Inrtia Analysis Command to do analysis. selected Hollow section Type with 0.75 mm thickness

Analysis of Section here Shown, the MOI max and MOI min here given, we have to take MOI min for Section Modulus Calculation as for Design for Safety.

Distance of Neutral Axis to the Outermost fiber is y

Total Distance under Consideration of loding is 876 mm

so here y=876.46/2 = 438.23 mm

Z=MOI min/y

=(2.803975x10^5)/438.23

Z=639.841 mm^3

now to optimize Section Modulus lets increase depth of inner panel by 0.5 mm.

so created closed sketch by offsetting inner panel 0.5 mm downward and did Analysis of new Section

Sction Modulus (Z)

Z=2.84004/438.23

=648.062 mm^3

So here we Can increase Strength of Hood Panel by incrasing depth hood inner panel without incrasing much material.